A natural number is always a rational number .
Yes, it is.
No.A rational times an irrational is never rational. It is always irrational.
Yes, the sum is always rational.
The product of an irrational number and a rational number, both nonzero, is always irrational
It is always rational.
No, and I can prove it: -- The product of two rational numbers is always a rational number. -- If the two numbers happen to be the same number, then it's the square root of their product. -- Remember ... the product of two rational numbers is always a rational number. -- So the square of a rational number is always a rational number. -- So the square root of an irrational number can't be a rational number (because its square would be rational etc.).
No. It's always irrational.
The product of a rational and irrational number can be rational if the rational is 0. Otherwise it is always irrational.
Yes, always. That is the definition of a rational number.
If an irrational number is added to, (or multiplied by) a rational number, the result will always be an irrational number.
Actually the product of a nonzero rational number and another rational number will always be rational.The product of a nonzero rational number and an IRrational number will always be irrational. (You have to include the "nonzero" caveat because zero times an irrational number is zero, which is rational)